Neural network pruning techniques can substantially reduce the computational cost of applying convolutional neural networks (CNNs). Common pruning methods determine which convolutional filters to remove by ranking the filters individually, i.e., without taking into account their interdependence. In this paper, we advocate the viewpoint that pruning should consider the interdependence between series of consecutive operators. We propose the LongEst-chAiN (LEAN) method that prunes CNNs by using graph-based algorithms to select relevant chains of convolutions. A CNN is interpreted as a graph, with the operator norm of each operator as distance metric for the edges. LEAN pruning iteratively extracts the highest value path from the graph to keep. In our experiments, we test LEAN pruning on several image-to-image tasks, including the well-known CamVid dataset, and a real-world X-ray CT dataset. Results indicate that LEAN pruning can result in networks with similar accuracy, while using 1.7-12x fewer convolutional filters than existing approaches.